CN107204780A - The merging BP decoding algorithms and device of polar LDPC concatenated codes - Google Patents
The merging BP decoding algorithms and device of polar LDPC concatenated codes Download PDFInfo
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
- H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
- H03M13/1105—Decoding
- H03M13/1111—Soft-decision decoding, e.g. by means of message passing or belief propagation algorithms
- H03M13/1117—Soft-decision decoding, e.g. by means of message passing or belief propagation algorithms using approximations for check node processing, e.g. an outgoing message is depending on the signs and the minimum over the magnitudes of all incoming messages according to the min-sum rule
- H03M13/112—Soft-decision decoding, e.g. by means of message passing or belief propagation algorithms using approximations for check node processing, e.g. an outgoing message is depending on the signs and the minimum over the magnitudes of all incoming messages according to the min-sum rule with correction functions for the min-sum rule, e.g. using an offset or a scaling factor
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
- H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
- H03M13/1191—Codes on graphs other than LDPC codes
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/29—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
- H03M13/2906—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes using block codes
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Abstract
The present invention provides a kind of the merging BP decoding algorithms and device of polar LDPC concatenated codes.The present invention includes：Initialization module, iterative calculation module and hard decision module, described initialization module are included the vector initialising multiplier for log-likelihood ratio information of channel observation；The iterative calculation module includes the multiplier group that the variable with factor graph, check-node, basic computational ele- ment and factor of influence are schemed relative to Tanner；The hard decision module includes the hard decision unit for obtaining decoding result.The present invention with traditional algorithm iterations identical in the case of, by setting factor of influence, result in the error performance for being substantially better than conventional method, and computation complexity does not have very big difference.
Description
Technical field：
The present invention relates to a kind of merging BP decoding algorithms of polar-LDPC concatenated codes and device, belong to computer communication neck
Domain.
Background technology：
In awgn channel environment, forefathers are respectively to polarization code and Low Density Parity Check (LDPC) code
Belief Propagation (BP) decoding algorithm had extensively and in-depth study.In addition, code cascading scheme is also because it is missed
Code performance has the less advantage of safe distance and is widely studied.In the research of forefathers, various code character closes bag
The different concatenated schemes for including the polarization code in the present invention and LDPC code are all discussed.But forefathers fail two-stage decoding device
Similitude use, the present invention in, we using two-stage code BP interpretation methods similitude, it is proposed that one kind innovation
Point thinking, by the cascade of figure, one is merged into by decoder, allows one yard of circulation of LDPC and polarization code sequentially to carry out successively,
Form a complete cyclic process.
The content of the invention
The purpose of the present invention is to be directed to problems of the prior art, proposes a kind of merging of polar-LDPC concatenated codes
BP decoding algorithms and device, change the Iterative path of information, and improve the accuracy of decoding.
Above-mentioned purpose is achieved through the following technical solutions：
A kind of merging BP decoding algorithms of polar-LDPC concatenated codes, this method comprises the following steps：
(1) channel observation vector y is initialized as to the probabilistic information of each bit word by formula (1),
In formula (1)：L(xj) for the log-likelihood ratio of each yard of bit, N0For channel
Average noise power；
(2) by L (sj) as the information of variable node on Tanner figures, and with min-sum method meters on check-node
Calculate once, and the value after calculating is returned to all variable nodes, variable node is collected all check-nodes being attached thereto and transmitted
Information；
(3) a part of variable node being connected with factor graph, regard its probabilistic information as most right (n+1) single order of factor graph
Left information Ln+1,j, factor graph is according to formula (2), formula (3), formula (4), formula (5) calculating except institute on the first rank external cause subgraph
There is the left and right information of rank；
Li,j=g (Li+1,2j-1,Li+1,2j+Ri,j+N/2), formula (2),
Li,j+N/2=g (Ri,j,Li+1,2j-1)+Li+1,2j, formula (3),
Ri+1,2j-1=g (Ri,j,Li+1,2j+Ri,j+N/2), formula (4),
And Ri+1,2j=g (Ri,j,Li+1,2j-1)+Ri,j+N/2, formula (5),
It is N (N=2 to code length in formula (2), formula (3), formula (4), formula (5)n) polar codes, each node
There are two kinds of mutual informations, the information of j-th of node of the i-th rank of its n+1 rank factor graph is referred to as left information (Li,j) and it is right
Information (Ri,j)；Function g (x, y)=sign (x) sign (y) min (| x |, | y |)；
(4) formula L (s are passed through in the junction of figurej)=a × Rn+1,j+L(sj) update code word information, wherein a is one
Adjust the factor of influence of two parts information accounting；
(5) using step (2), step (3), step (4) as once overall loop iteration, calculate I times, finally because
The left information L of the first rank is calculated on the left of subgraph1,jAnd a hard decision is carried out to it, obtain decoding result.
L (s in the merging BP decoding algorithms of described polar-LDPC concatenated codes, step (2)j)=L (xj+M-N), this L
(sj) and L (xj+M-N) still it is the log-likelihood ratio defined before.
A kind of merging BP decoding apparatus of polar-LDPC concatenated codes, the device includes：Initialization module, iterative calculation mould
Block and hard decision module, described initialization module were included channel observation vector initialising multiplying for log-likelihood ratio information
Musical instruments used in a Buddhist or Taoist mass；The iterative calculation module includes variable, check-node, the basic computational ele- ment schemed relative to Tanner with factor graph
And the multiplier group of factor of influence；The hard decision module includes the hard decision unit for obtaining decoding result.
Beneficial effect：
Compared with prior art, the invention has the advantages that：
Advantage of the invention is that a kind of decoding scheme of the merging based on figure is proposed, and it is complicated to remain BP algorithm
The low advantage of degree, with traditional algorithm iterations identical in the case of, by setting factor of influence, result in substantially excellent
In the error performance of conventional method, and computation complexity does not have very big difference.
Brief description of the drawings
Fig. 1：The merging decoding schematic diagram for the merging BP decoding algorithms based on polar-LDPC concatenated codes that the present invention is provided；
Fig. 2：Code check is 0.25, and ISN code length is 1024, when outer code code length is 2048, merges decoding algorithm using the present invention
With the ber curve figure of traditional decoding algorithm under Different Effects factor value；
Fig. 3：Code check is 0.6, and ISN code length is 1024, when outer code code length is 1280, merges decoding algorithm using the present invention
With the ber curve figure of traditional decoding algorithm under Different Effects factor value；
Fig. 4：The merging decoding hardware frame for the merging BP decoding algorithms based on polar-LDPC concatenated codes that the present invention is provided
Structure schematic diagram；
Fig. 5：The present invention merges decoding algorithm and the computation complexity of the tradition separation each iteration of decoding algorithm compares.
Embodiment
With reference to embodiment, the present invention is furture elucidated, it should be understood that following embodiments are only used for
The bright present invention rather than limitation the scope of the present invention.
Embodiment 1：
A kind of merging BP decoding algorithms of polar-LDPC concatenated codes, this method comprises the following steps：
(1) channel observation vector y is initialized as to the probabilistic information of each bit word by formula (1),
In formula (1)：L(xj) for the log-likelihood ratio of each yard of bit,
N0For the average noise power of channel；
(2) by L (sj) as the information of variable node on Tanner figures, and with min-sum method meters on check-node
Calculate once, and the value after calculating is returned to all variable nodes, variable node is collected all check-nodes being attached thereto and transmitted
Information；
(3) a part of variable node being connected with factor graph, regard its probabilistic information as most right (n+1) single order of factor graph
Left information Ln+1,j, factor graph is according to formula (2), formula (3), formula (4), formula (5) calculating except institute on the first rank external cause subgraph
There is the left and right information of rank；
Li,j=g (Li+1,2j-1,Li+1,2j+Ri,j+N/2), formula (2),
Li,j+N/2=g (Ri,j,Li+1,2j-1)+Li+1,2j, formula (3),
Ri+1,2j-1=g (Ri,j,Li+1,2j+Ri,j+N/2), formula (4),
And Ri+1,2j=g (Ri,j,Li+1,2j-1)+Ri,j+N/2, formula (5),
It is N (N=2 to code length in formula (2), formula (3), formula (4), formula (5)n) polar codes, each node
There are two kinds of mutual informations, the information of j-th of node of the i-th rank of its n+1 rank factor graph is referred to as left information (Li,j) and it is right
Information (Ri,j)；Function g (x, y)=sign (x) sign (y) min (| x |, | y |)；
(4) formula L (s are passed through in the junction of figurej)=a × Rn+1,j+L(sj) update code word information, wherein a is one
Adjust the factor of influence of two parts information accounting；
(5) using step (2), step (3), step (4) as once overall loop iteration, calculate I times, finally because
The left information L of the first rank is calculated on the left of subgraph1,jAnd a hard decision is carried out to it, obtain decoding result.
L (s in the merging BP decoding algorithms of described polar-LDPC concatenated codes, step (2)j)=L (xj+M-N), this L
(sj) and L (xj+M-N) still it is the log-likelihood ratio defined before.
A kind of merging BP decoding apparatus of polar-LDPC concatenated codes, the device includes：Initialization module, iterative calculation mould
Block and hard decision module, described initialization module were included channel observation vector initialising multiplying for log-likelihood ratio information
Musical instruments used in a Buddhist or Taoist mass；The iterative calculation module includes variable, check-node, the basic computational ele- ment schemed relative to Tanner with factor graph
And the multiplier group of factor of influence；The hard decision module includes the hard decision unit for obtaining decoding result.
A polar-LDPC concatenated codes coding and Decoding model on awgn channel is set up in the present embodiment and carries out mould
Intend operation.In this coding and decoding model, ISN (polar codes) s code length is that information bit quantity is K in N, vectorial u to be encoded,
Therefore ISN code check is K/N, and remaining N-K conduct freezes position (frozen bits) and be all set to 0.The exponent number of factor graph is
N+1, wherein N=2n.The cataloged procedure of ISN can be expressed as
S=uGN,
Its generator matrix GNIt can be represented with factor graph, the formula of construction generator matrix is(It is n Kronecker product operation).Outer code x coding needs to be configured to m × M of LDPC code check matrix H, wherein
M is outer code code length, and m is verification bit quantity (m=M-N).Check matrix construction our use unit matrix cyclic shift method
Construction.Code word is modulated by BPSK and transmitted on awgn channel, when analog channel environment, chooses several Eb/N0's
Situation is used as simulated channel ambient parameter.During decoding, same code word is passed through the decoding situation of two decoders separated respectively
It is compared, compares under emulation with the decoding situation in the case of the merging decoder of several Different Effects factor values
Bit error rate situation (such as Fig. 2,3).
In terms of hardware structure, the merging BP decoding algorithms based on polar-LDPC concatenated codes used in the present embodiment it is hard
Part framework is shown in Fig. 1, including channel observation information initialization section, iterative calculation part and hard decision part.
Specifically, decoder is received after channel observation information, and first they are once initialized, each is multiplied
With -4/N0To obtain the initial value of its log-likelihood ratio information.
In iterative calculation part, the information of code word is transmitted to the Tanner modules progress once verification calculating on right side first,
Basic computational ele- ment to the left in incoming factor graph carries out the calculating of each left and right information of node again, wherein, the right side of the first rank
Channel capacity information is initialized when information is by encoding, and it is infinity, information bit initialization to freeze the information initializing of position
For 0.When information returns to the junction of figure, the collection of all information is done once at the node of code word, one is set herein
Individual factor of influence, adjusts two parts information accounting, and be used as using this information the initial value of next iteration.
Claims (3)
1. a kind of merging BP decoding algorithms of polar-LDPC concatenated codes, it is characterised in that：This method comprises the following steps：
(1) channel observation vector y is initialized as to the probabilistic information of each bit word by formula (1),
In formula (1)：L(xj) for the log-likelihood ratio of each yard of bit,
N0For the average noise power of channel；
(2) by L (sj) calculate one with min-sum methods as the information of variable node on Tanner figures, and on check-node
It is secondary, and the value after calculating is returned to all variable nodes, variable node collects the letter that all check-nodes being attached thereto are transmitted
Breath；
(3) a part of variable node being connected with factor graph, using its probabilistic information as most right (n+1) single order of factor graph left letter
Cease Ln+1,j, factor graph is according to formula (2), formula (3), formula (4), formula (5) calculating except all ranks on the first rank external cause subgraph
Left and right information；
Li,j=g (Li+1,2j-1,Li+1,2j+Ri,j+N/2), formula (2),
Li,j+N/2=g (Ri,j,Li+1,2j-1)+Li+1,2j, formula (3),
Ri+1,2j-1=g (Ri,j,Li+1,2j+Ri,j+N/2), formula (4),
And Ri+1,2j=g (Ri,j,Li+1,2j-1)+Ri,j+N/2, formula (5),
It is N (N=2 to code length in formula (2), formula (3), formula (4), formula (5)n) polar codes,
Each node has two kinds of mutual informations, and the information of j-th of node of the i-th rank of its n+1 rank factor graph is referred to as left letter
Cease (Li,j) and right information (Ri,j)；Function g (x, y)=sign (x) sign (y) min (| x |, | y |)；
(4) formula L (s are passed through in the junction of figurej)=a × Rn+1,j+L(sj) update code word information, wherein a be one adjustment
The factor of influence of two parts information accounting；
(5) using step (2), step (3), step (4) as once overall loop iteration, calculate I times, it is finally left in factor graph
Side calculates the left information L of the first rank1,jAnd a hard decision is carried out to it, obtain decoding result.
2. the merging BP decoding algorithms of polar-LDPC concatenated codes according to claim 1, it is characterised in that：Step (2)
In L (sj)=L (xj+M-N), this L (sj) and L (xj+M-N) still it is the log-likelihood ratio defined before.
3. a kind of merging BP decoding apparatus of polar-LDPC concatenated codes, it is characterised in that：The device includes：Initialization module,
Module and hard decision module are iterated to calculate, described initialization module includes channel observation is vector initialising for log-likelihood ratio
The multiplier of information；The iterative calculation module include relative to Tanner scheme and the variable of factor graph, check-node, it is basic based on
Calculate the multiplier group of unit and factor of influence；The hard decision module includes the hard decision unit for obtaining decoding result.
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| CN108809329A (en) * | 2018-05-03 | 2018-11-13 | 东南大学 | A kind of configuration method for the BP decoders that can handle polarization code and LDPC code simultaneously |
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| CN110166167A (en) * | 2018-02-14 | 2019-08-23 | 华为技术有限公司 | Method, the method for decoding, encoding device and the decoding equipment of coding |
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| WO2020052537A1 (en) * | 2018-09-14 | 2020-03-19 | 华为技术有限公司 | Decoding method and device for polar codes |
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| CN109547156A (en) * | 2018-10-18 | 2019-03-29 | 北京理工大学 | Non-coherent detection methods, device and the electronic equipment of polar short code |
| CN112104412A (en) * | 2020-11-17 | 2020-12-18 | 四川九洲电器集团有限责任公司 | Accelerator suitable for low-orbit satellite broadband communication |
| CN112104412B (en) * | 2020-11-17 | 2021-02-02 | 四川九洲电器集团有限责任公司 | Accelerator suitable for low-orbit satellite broadband communication |
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